Tissue viscoelasticity can be imaged by monitoring shear wave propagation inside of tissue. Shear wave motion, as a function of time and space, can be analyzed in the temporal- and spatial-frequency domain by performing a Fourier transform. This domain is often called “k-space.” It is known that a k-space representation of a shear wave is a useful tool for estimating shear wave velocity and applying directional filters.
The shear wave velocities, c, at different frequencies can be identified by finding the local maxima in k-space and using the temporal frequency, f, and spatial frequency,
      k    =          1      λ        ,coordinates,
      c    =                  f        k            =              f        ⁢                                  ⁢        λ              ,where λ is the wavelength of the shear wave. A unique feature of k-space analysis is that waves of different modes can be separated even when they are at the same frequency. This is also useful since multiple modes can exist simultaneously when tissue vibrates.
One important advantage of k-space analysis is that the waves propagating in opposite directions can be differentiated. This is especially useful in mechanical-wave-based tissue elastography methods, since wave reflections can be common in certain tissues. In fact, directional filtering is based on this feature because it only selects the energy in specific locations in k-space and then transform back to time and spatial domain, to remove waves travelling in unwanted directions.
Though, as addressed above, k-space analysis for estimating wave velocity is a useful tool, the accuracy of the estimates can vary. For example, soft tissues are inherently viscoelastic. Thus, as waves travel through soft tissues, the energy in the wave is diminished, causing its amplitude to decrease. Without a more accurate complex modulus of the tissue, velocity estimates are of limited clinical utility.
Therefore, it would be desirable to have a system and method for determining a complex modulus of the tissue that can be used in clinical analysis of tissue.